By Toshiyuki Shiozawa
Waves in Relativistic Electron Beams presents a complicated process classical electrodynamics with software to the new release of high-power coherent radiation within the microwave to optical-wave areas. in particular, it presents readers with the fundamentals of complex electromagnetic thought and relativistic electrodynamics, guiding them step-by-step during the idea of free-electron lasers. The theoretical therapy all through this publication is absolutely constructed via the standard third-dimensional vector calculus. This booklet might be suggested as a graduate-level textbook or a reference publication within the fields of complicated electromagnetic idea, relativistic electrodynamics, beam physics and plasma sciences.
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Extra resources for Classical Relativistic Electrodynamics: Theory of Light Emission and Application to Free Electron Lasers
6) denote the change in frequency or the Doppler shift in frequency produced by the relative motion of two inertial systems. As is evident from the above discussion, in relativity, the frequency and wave numbers are transformed as a cluster, or more precisely, as a four-vector in the same manner as the space-time coordinates. With the aid of the transformation formula for frequency, we can find the constitutive relations for a moving temporally dispersive medium or a moving medium with frequency dispersion.
13) with t lr--r'l ,=f-. 14) where ( denotes the retarded time. which is defined as the time at which the signal 26 I. Basic Electromagnetic Theory arriving at the position r at the time t is emitted at the position r'. Note that the signal emitted at the position r' is propagated at the speed u over the distance between the two positions. 15) 1 r p(r', t') dv. 4). 1 with the aid of the Fourier analysis described in the preceding section. 3) p(r,w) = J_:p(r,t)e-jwrdt. 10 Electromagnetic Radiation in Unbounded Space E(r,w) = -V;jJ(r,w)- jwA(r,w).
4R 2. 6 Integral Representation of the Maxwell Equations in Moving Systems Consider a closed contour C moving with constant velocity v relative to the inertial system /, and an open surface S bounded by the closed contour C, as shown in Fig. 2. Then, let us discuss the integral representation of the Maxwell equations for the closed contour C and the open surface S. First, we consider Faraday's induction law, which states that if the amo unt of the magnetic flux linking the closed contour C is temporally changed, the electromotive force is produced around C with the magnitude equal to the negative time rate of change of the magnetic flux linking the contour C.
Classical Relativistic Electrodynamics: Theory of Light Emission and Application to Free Electron Lasers by Toshiyuki Shiozawa